/tags/2014-winter/index.xml 2014 Winter - McGill Statistics Seminars

2014 Winter

  • Calibration of computer experiments with large data structures

    Derek Bingham · Jan 24, 2014

    Date: 2014-01-24

    Time: 15:30-16:30

    Location: Salle 1355, pavillon André-Aisenstadt (CRM)

    Abstract:

    Statistical model calibration of computer models is commonly done in a wide variety of scientific endeavours. In the end, this exercise amounts to solving an inverse problem and a form of regression. Gaussian process model are very convenient in this setting as non-parametric regression estimators and provide sensible inference properties. However, when the data structures are large, fitting the model becomes difficult. In this work, new methodology for calibrating large computer experiments is presented. We proposed to perform the calibration exercise by modularizing a hierarchical statistical model with approximate emulation via local Gaussian processes. The approach is motivated by an application to radiative shock hydrodynamics.

  • An introduction to stochastic partial differential equations and intermittency

    Raluca Balan · Jan 10, 2014

    Date: 2014-01-10

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In a seminal article in 1944, Itô introduced the stochastic integral with respect to the Brownian motion, which turned out to be one of the most fruitful ideas in mathematics in the 20th century. This lead to the development of stochastic analysis, a field which includes the study of stochastic partial differential equations (SPDEs). One of the approaches for the study of SPDEs was initiated by Walsh (1986) and relies on the concept of random-field solution for equations perturbed by a space-time white noise (or Brownian sheet). This concept allows us to investigate the dynamical changes in the probabilistic behavior of the solution, simultaneously in time and space. These developments will be reviewed in the first part of the talk. The second part of the talk will be dedicated to some recent advances in this area, related to the existence of a random-field solution for some classical SPDEs (like the stochastic heat equation) perturbed by a colored'' noise, which behaves in time like the fractional Brownian motion. When this solution exists, it exhibits a strong form of intermittency,’’ a property which was originally introduced in the physics literature for describing random fields whose values develop very large peaks. This talk is based on some recent joint work with Daniel Conus (Lehigh University).